A047352 Numbers that are congruent to {0, 2} mod 7.

0, 2, 7, 9, 14, 16, 21, 23, 28, 30, 35, 37, 42, 44, 49, 51, 56, 58, 63, 65, 70, 72, 77, 79, 84, 86, 91, 93, 98, 100, 105, 107, 112, 114, 119, 121, 126, 128, 133, 135, 140, 142, 147, 149, 154, 156, 161, 163, 168, 170

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers k such that k^2/7 + k*(k + 1)/14 = k*(3*k + 1)/14 is a nonnegative integer. - Bruno Berselli, Feb 14 2017

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A005009, A030308.

Programs

Mathematica

LinearRecurrence[{1,1,-1},{0,2,7},50] (* Harvey P. Dale, Oct 16 2022 *)

PARI

forstep(n=0,200,[2,5],print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

Formula

a(n) = 7*n - a(n-1) - 12 with a(1)=0. Also: a(n) = a(n-1) + a(n-2) - a(n-3). - Vincenzo Librandi, Aug 05 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=2 and b(k)=A005009(k-1) for k>0. - Philippe Deléham, Oct 17 2011

G.f.: x^2*(2 + 5*x)/((1 + x)*(1 - x)^2). - R. J. Mathar, Dec 04 2011

a(n) = floor((7/3)*floor(3*n/2)). - Clark Kimberling, Jul 04 2012

E.g.f.: 5 + ((14*x - 17)*exp(x) - 3*exp(-x))/4. - David Lovler, Aug 31 2022